Can a proxy appoint proxy?

not at all

Proxy is agent and agent can't appoint his agent 

hence ans is no

As per 176 of Co. Act, 1956

Any member of a company entitled to attend and vote at a meeting of the company shall be entitled to appoint another person (whether a member or not) as his proxy to attend and vote instead of himself; but a proxy so appointed shall not have any right to speak at the meeting.

As per Clause 57: of  Table A of Schedule I  “regulations for management of a company limited by shares” In the case of joint holders, the vote of the senior who tenders a vote, whether in person or by proxy, shall be accepted to the exclusion of the votes of the other joint holders.

For this purpose, seniority shall be determined by the order in which the names stand in the register of members.

Clause 62: An instrument appointing a proxy shall be in either of the forms in Schedule IX to the Act or a form as near thereto as circumstances admit.

And

• a proxy shall not be entitled to vote except on a poll.
  
•  
• a member of a private company shall not be entitled to appoint more than one proxy to attend on the same occasion.
•  
• a proxy need not be a member.

A proxy cannot appoint another proxy because he has only representational powers of pricipals.